484? On the Entrance Passages in the Pyramids of Gizeh. 



Calculations. 

 Por. of a Draconis for 1839. 



R.A. 1830 = 13 h 59 m 46 s -6 Due 1830 = 65° 11' 26" (seeAstr.Soc.Cat.) 

 Precession + 9 years = + \4''6 Pre.+ 9years-=— 2 36 



14 T2 65 8 50 = S for 1839. 



Reduced to arc 210° 0' 18" = « 



Precession in longitude for + 1 year, epoch 1800 , -f 50"*22350 



Variation for 2000 years backwards, to obtain a mean rate \ _ n .(uqqr 



of precession for 4000 J 



+50 -17464 



Multiply by years —4000 



Precession in long. = -200697"*56 = — 55° 44' 57"*56 —200697*56000 



or correctly enough for the purpose 55° 44' 58" 



P the present place of the north 



pole. 

 P' its place 4000 years ago. 

 a, the star cc Draconis. 

 its projection on the equinoctial. 

 rsi/3 = 210 o 0'18" = « 



T £: = 180 



rfi: /3 = 30 18 = angle 



£ P« 

 In spherical triangle P II P'. 

 Given angle PnP= 55° 44' 58". 

 P II = P' n = obliquity of ecliptic 

 at a, mean epoch, 2000 years 

 back. 

 Obliquity ISOOy =23° 27' 55" 

 Var. for —20007 = + 1 31 



23 29 26 — obliquity to be, and = Pn 

 Solution of triangle II PP'. 

 Sin | Pn P' — sin 27°52 / 29" ... 96698186 Tan 27° 52' 29"... 9*7233852 



Sin obliquity 9*6005350 Cos obliquity ...99624319 



Sin ^PP'=10°44 / 25' 



Required 1st side PP'. 



2nd angle P'P IT. 



pn. 



9-2703536 



PP' = 21°28'50". 

 -vpn = 90 o . 

 :fiP«=30 o , 18" 



Cotan64°7'22"... 9-6858171 

 Angle P'P n= 64° 7' 22" 



« P n = 59 59 42 

 FPn = 64 7 22 

 P'P«= 4 7 40 

 Co E . 4° 7' 40" 9-9988720 

 Tan 21 28 50 9*5949652 

 Tana'2125 48 9-5938372" 

 24 51 10 



In triangle P'P cc given PP' =21° 28' 50'' 



P«=24 51 10 =90- 

 Angle P 1 P cc = 4 7 40 

 Required a, P'. 



Cos 21 28 50 



Cos 2 25 22 



Cos 21 25 48 

 CosP'« = 2 51 15 



9-9687359 

 9-9996116 

 9*9683475 

 9*9688865 

 99994610 



a" 2 25 22 



Note. — These calculations, which take in all the influence 

 of the secular variations of precession, &c, may be considered 

 quite equal, in point of precision, to any direct observation 

 that an Egyptian astronomer of that date could have made. 



